{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Transformer Model\n",
    "In this notebook, we show an example of how Transformer can be used with darts.\n",
    "If you are new to darts, we recommend you first follow the `darts-intro.ipynb` notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fix python path if working locally\n",
    "from utils import fix_pythonpath_if_working_locally\n",
    "fix_pythonpath_if_working_locally()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import shutil\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from tqdm import tqdm_notebook as tqdm\n",
    "\n",
    "from torch.utils.tensorboard import SummaryWriter\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from darts import TimeSeries\n",
    "from darts.dataprocessing.transformers import Scaler\n",
    "from darts.models import TransformerModel, ExponentialSmoothing\n",
    "from darts.metrics import mape\n",
    "from darts.utils.statistics import check_seasonality, plot_acf\n",
    "from darts.datasets import AirPassengersDataset, SunspotsDataset\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "import logging\n",
    "logging.disable(logging.CRITICAL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Air Passengers Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we will test the performance of the transformer architecture on the 'air passengers' dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read data:\n",
    "series = AirPassengersDataset().load()\n",
    "\n",
    "# Create training and validation sets:\n",
    "train, val = series.split_after(pd.Timestamp('19590101'))\n",
    "\n",
    "# Normalize the time series (note: we avoid fitting the transformer on the validation set)\n",
    "# Change name\n",
    "scaler = Scaler()\n",
    "train_scaled = scaler.fit_transform(train)\n",
    "val_scaled = scaler.transform(val)\n",
    "series_scaled = scaler.transform(series)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"the 'air passengers' dataset has 144 data points\""
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'the \\'air passengers\\' dataset has {} data points'.format(df.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We train a standard transformer architecture with default hyperparameters, tweaking only two of them:\n",
    "\n",
    "* _d\\_model_, the input dimensionality of the transformer architecture (*after* performing time series embedding). Its default value is 512. We lower the value from 512 to 64, since it is hard to learn such an high-dimensional representation from an univariate time series\n",
    "* _nhead_, the number of heads in the multi-head attention mechanism. We increase the value from 8 to 32. This means that we compute multi-head attention with 32 heads of size _d\\_model_/_nhead_=64/32=2 each. This way, we obtain low-dimensional heads that are hopefully suitable to learn from univariate time series\n",
    "\n",
    "The goal is to perform one-step forecasting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "my_model = TransformerModel(\n",
    "    input_chunk_length = 12,\n",
    "    output_chunk_length = 1,\n",
    "    batch_size = 32,\n",
    "    n_epochs = 400,\n",
    "    model_name = 'air_transformer',\n",
    "    log_tensorboard=True,\n",
    "    nr_epochs_val_period = 10,\n",
    "    d_model = 32,\n",
    "    nhead = 16,\n",
    "    num_encoder_layers = 3,\n",
    "    num_decoder_layers = 3,\n",
    "    dim_feedforward = 512,\n",
    "    dropout = 0.1,\n",
    "    activation = \"relu\",\n",
    "    random_state=42,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false,
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "241a70bfeb83402c8f113d9aa1a253dd",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=400.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training loss: 0.0027, validation loss: 0.0172, best val loss: 0.0067\n"
     ]
    }
   ],
   "source": [
    "my_model.fit(series=train_scaled, val_series=val_scaled, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the predictions on the validation set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, by using the \"current\" model - i.e., the model at the end of the training procedure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#this function evaluates a model on a given validation set for n time-steps\n",
    "def eval_model(model, n, series, val_series):\n",
    "    pred_series = model.predict(n=n)\n",
    "    plt.figure(figsize=(8,5))\n",
    "    series.plot(label='actual')\n",
    "    pred_series.plot(label='forecast')\n",
    "    plt.title('MAPE: {:.2f}%'.format(mape(pred_series, val_series)))\n",
    "    plt.legend();\n",
    "    \n",
    "eval_model(my_model, 26, series_scaled, val_scaled)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, by using the best model obtained over training, according to validation loss:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loading model_best_220.pth.tar\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "best_model = TransformerModel.load_from_checkpoint(model_name='air_transformer', best=True)\n",
    "eval_model(best_model, 26, series_scaled, val_scaled)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's backtest our `Transformer` model to evaluates its performance at a forecast horizon of 6 months:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4ea2cff2f9a147e0bf66e22b7c3c3cad",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=18.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "backtest_series = my_model.historical_forecasts(series = series_scaled,\n",
    "                                                start = pd.Timestamp('19590101'), \n",
    "                                                forecast_horizon = 6,\n",
    "                                                retrain = False,\n",
    "                                                verbose = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAPE: 6.19%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "series_scaled.plot(label='actual', lw=2)\n",
    "backtest_series.plot(label='backtest', lw=2)\n",
    "plt.legend()\n",
    "plt.title('Backtest, starting Jan 1959, with a 6-months horizon');\n",
    "print('MAPE: {:.2f}%'.format(mape(scaler.inverse_transform(series_scaled), \n",
    "                                  scaler.inverse_transform(backtest_series))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Monthly Sun spots Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's test the transformer architecture on a more complex dataset, the 'monthly sunspots'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "series_sunspot = SunspotsDataset().load()\n",
    "\n",
    "series_sunspot.plot()\n",
    "check_seasonality(series_sunspot, max_lag=240)\n",
    "\n",
    "train_sp, val_sp = series_sunspot.split_after(pd.Timestamp('19401001'))\n",
    "\n",
    "scaler_sunspot = Scaler()\n",
    "train_sp_scaled = scaler_sunspot.fit_transform(train_sp)\n",
    "val_sp_scaled = scaler_sunspot.transform(val_sp)\n",
    "series_sp_scaled = scaler_sunspot.transform(series_sunspot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"the 'monthly sun spots' dataset has 2820 data points\""
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'the \\'monthly sun spots\\' dataset has {} data points'.format(df2.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's perform one-step ahead forecasting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "my_model_sp = TransformerModel(\n",
    "    batch_size = 32,\n",
    "    input_chunk_length = 125,\n",
    "    output_chunk_length = 36,\n",
    "    n_epochs = 20,\n",
    "    model_name = 'sun_spots_transformer',\n",
    "    log_tensorboard=True,\n",
    "    nr_epochs_val_period = 5,\n",
    "    d_model = 32,\n",
    "    nhead = 8,\n",
    "    num_encoder_layers = 4,\n",
    "    num_decoder_layers = 4,\n",
    "    dim_feedforward = 512,\n",
    "    dropout = 0.1,\n",
    "    random_state=42,\n",
    "    optimizer_kwargs={'lr': 1e-3}\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "87f9a4b59f92433b85969af1aceff3c5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=20.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training loss: 0.0105, validation loss: 0.0253, best val loss: 0.0232\n"
     ]
    }
   ],
   "source": [
    "my_model_sp.fit(series=train_sp_scaled, val_series=val_sp_scaled, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loading model_best_10.pth.tar\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "78d78e419b494ebc9c4066666b75e1c2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=49.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bf6fc5ed374e4a9489d38e35428fa957",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=49.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Transformer MAPE: 67.35159696769936\n",
      "ETS MAPE: 593.7817328101518\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this function is used to backtest the model at a forecasting horizon of three years (36 months)\n",
    "def backtest(testing_model):\n",
    "    # Compute the backtest predictions with the two models\n",
    "    pred_series = testing_model.historical_forecasts(series = series_sp_scaled, \n",
    "                                                     start = pd.Timestamp('19401001'), \n",
    "                                                     forecast_horizon = 36,\n",
    "                                                     stride = 10,\n",
    "                                                     retrain = False,\n",
    "                                                     verbose = True)\n",
    "    \n",
    "    pred_series_ets = ExponentialSmoothing().historical_forecasts(series = series_sp_scaled,\n",
    "                                                                  start = pd.Timestamp('19401001'), \n",
    "                                                                  forecast_horizon = 36,\n",
    "                                                                  stride = 10,\n",
    "                                                                  retrain = True,\n",
    "                                                                  verbose = True)\n",
    "    val_sp_scaled.plot(label = 'actual')\n",
    "    pred_series.plot(label = 'our Transformer')\n",
    "    pred_series_ets.plot(label = 'ETS')\n",
    "    plt.legend();\n",
    "    print(\"Transformer MAPE:\", mape(pred_series, val_sp_scaled))\n",
    "    print(\"ETS MAPE:\", mape(pred_series_ets, val_sp_scaled))\n",
    "    \n",
    "best_model_sp = TransformerModel.load_from_checkpoint(model_name='sun_spots_transformer', best=True)\n",
    "backtest(best_model_sp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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